7.2 Day 0

7.2 Day 0

We're skipping 7.1 ​

Ms. Swetlic Algebra 2 Essentials​

What will you be learning in Ch. 7??

...all about RATIONAL FUNCTIONS​

Rational functions are equations that

can be expressed as one polynomial

divided by another polynomial.

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Here are a few examples

of what they look like -->​

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They have a vertical asymptote (blue dotted line shown)

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AND a horizontal asymptote (red dotted line shown).

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The graph of a rational function is called a HYPERBOLA.

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Multiple Choice

Which graph below is a hyperbola?

Multiple Choice

Which statement is true?

• Hyperbolas have a vertical and a horizontal asymptote.

• Hyperbolas have vertical asymptotes only.

• Hyperbolas have horizontal asymptotes only.

• Hyperbolas do not have any asymptotes.

​This is the general form of a rational equation.

Maybe write this down to help with the next couple slides :)​

​The "k" value tells you the horizontal asymptote.

y = k​

​​The "h" value tells you the vertical asymptote.

x = h​

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​Look carefully at this example.

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The vertical asymptote is

x = 2​

(opposite of the -2 you see in the equation!)​

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The horizontal asymptote is y = 4​

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Multiple Choice

What are the equations of the horizontal and vertical asymptotes?

$$f\left(x\right)=\frac{1}{x-3}+5$$  

• Horizontal: y = -5

  Vertical: x = -3

• Horizontal: y = 5

  Vertical: x = -3

• Horizontal: y = 5

  Vertical: x = 3

• Horizontal: y = -5

  Vertical: x = 3

Fill in the Blanks

What is the equation of the HORIZONTAL asymptote for this equation? (k)

$f\left(x\right)=\frac{1}{x+2}+6$  

Fill in the Blanks

What is the equation of the VERTICAL asymptote for this equation? (h)

$f\left(x\right)=\frac{1}{x+2}+6$  

Poll

Good work! What do you think so far about rational functions?